I confess I assume that we do charge trucks an absurdly larger amount of money? Is why they have weigh stations between states?

That depends on what you consider "absurdly larger" - the fee is between $1,000-$2,000 depending on the state. In some states that's not much more than you'd be paying for a nice luxury car or large SUV.

https://www.truckinfo.net/research/license-costs-by-state

I confess I had a mistaken thought that weigh stations were akin to toll booths. That is, that fees were levied based on the weight.

I can think of several problems with that thought, taking it longer, of course. :(

I'm FAR from an expert, but you aren't totally misguided. That was the original intent once upon a time, now it's more about safety. They do weigh trucks to ensure they aren't going to destroy a bridge or damage roads if they're overweight for their route - but they're primarily checking a driver's log book to ensure they aren't over hours, the truck passes safety inspections, the driver isn't transporting illicit goods, etc.

I won't presume that I know how much we're taxing semis et al., but it's clear by the road wear that it's not enough, and most of the damage is not caused by everyday drivers.

Heavy vehicles also include garbage trucks, delivery trucks, and even busses which benefit everyone. Cars have only been widely adopted for about 100 years, and it's not clear that current trends can't be sustained for another 100.

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Also to prevent overweight unsafe loading, doing trafic safty inspections, smuggling prevention, and checking cargo especially to prevent cross border invasive species.

Yeah, I mostly knew these other reasons were a thing. I had not realized they were the only reason. I guess I was thinking of them more like a port of entry between states and assumed taxes were involved.